Polyphase impedance drop compensator



Feb. 23, 1937. E. L, HARDER 2,071,834 X POLYPHASB IMPEDANCE DROPco'urnusuon 7 Filed Dec. 13, 1935 I ig z wl 4'1 A /fl1: q a

vl'l'l'l'l'l'l '5 5'.

I 61 .1 14 12 2a 25' f I?! 3 Fig. 4

WITNESSES: INVENTOR Edwin L. Hrdgr.

Patented Feb. 23, 1937 UNITED STATES PATENT OFFICE Edwin L. Harder,Forest Hills, Pa, assignor to Westinghouse Electric a ManufacturingCompany. East Pittsburgh, Pa, a corporation of Pennsylvania ApplicationDecember 13, 1935, Serial No. 54,255

Claims.

My invention relates to alternating-current impedance drop compensators,and particularly to such compensators as used in connection with powertransformers to derive high-voltage quantities from the low-voltagecircuits of the transformers.

Such compensators commonly operate to produce compensating effectsequivalent in magnitude to impedance eflects of the transformers butopposite in sign, which are added to the low-voltage quantities of thetransformers to reproduce variables existing on the high-voltage sidesof the transformers. If the transformer connections are such that phasevoltages and phase currents are carried through the transformationwithout combinations between phases, the ordinary methods ofcompensation are directly applicable. However, transformer connectionsare frequently utilized which result in a different system of secondarypolyphase variables because of combinations of phase quantities. In suchapplications, quantities which are present as components of a singleprimary variable, usually appear as components of a numher of secondaryvariables, and the duplication of primary variables by compensationmethods is ordinarily not practical because of the excessive number ofinstrument transformers required. I have found, however, that byutilizing the symmetrical impedance relationships which can be obtainedin commercial transformer installations, high-voltage quantities may beduplicated from the low-voltage transformer circults by means ofcomparatively simple instrument transformer apparatus, and with comparatively small error.

It is accordingly an object of my invention to provide a novel method ofand apparatus for impedance drop compensation which will be applicableto polyphase transformer apparatus of the class in which a combinationof phase quantitles or other change of polyphase dimensions accompaniesthe transformation.

Other objects of my invention will become evident from the followingdetailed description taken in conjunction with the accompanying drawing,in which Figure 1 is a diagrammatic view of a polyphase transformer andimpedance drop compensator embodying my invention.

Fig. 2 is a vector diagram showing the relationship of voltages in thetransformer bank of Fig. 1.

Fig. 3 is a diagrammatic view of a modified potential transformerarrangement for use in the circuit of Fig. 1, and

Fig. 4 is a diagrammatic view of a simplified impedance drop compensatorwhich may be used in the practice of the invention.

Referring to Fig. 1 in detail, a polyphase highvoltage circuit I isconnected to a polyphase lowvoltage circuit 2 by means of a transformer3, shown as having star-connected high-voltage windings l with neutralungrounded and deltaconnected low-voltage windings 5. The highvoltagewindings 4 may be provided with a tapchanging device as indicateddiagrammatically at 6.

The transformer 3 may be any suitable form of stationary inductionapparatus capable of transforming polyphase power, such as a singlepolyphase transformer or a bank of singlephase transformers. It isessential, however, that the leakage impedance, on both primary andsecondary sides, have substantially the same value as to magnitude andphase angle, in all phases. It is also desirable that the mutualimpedance between primary windings and secondary windings be similarlysymmetrical in all phases, although some variation of mutual impedancemay be permitted without serious error.

A two-element power responsive device such as a wattmeter I is providedfor m a polyphase power quantity, such as the total real power flow, ofthe circuit I. The wattmeter I is provided with the usual current coils8 connected to be energized in accordance with phase currents of thehigh-voltage circuit by means of current transformers I0. The voltage orpotential coils 9 of the wattmeter I are connected to be energized fromthe low-voltage circuit 2 by means of a pair of potential transformers I2 and impedance drop compensators IS.

The potential transformers I 2 are each preferably so constructed as toproduce two secondary voltage components of equal magnitude and toprovide simultaneous adjustment of the ratios of these components to thevoltage impressed on the potential transformer primary windings. Forthis purpose, I preferably provide a mid-tap IS on the secondary windingof each potential transformer l2 and adjustable end-taps II on theprimary windings. It will be obvious, however, that other transformerarrangements having an equivalent function may be used.

The compensators I! may be of any suitable type, one example of which isdisclosed in my copending application Serial No. 52,121, filed November29, 1935, and assigned to the Westinghouse Electric 81 ManufacturingCompany. Such compensators comprise a mutual reactance section l8,consisting of two windings on a common core (not shown), and a mutualresistance section comprising a resistor 20 and a low-voltage auxiliarypotential transformer 2|. The adjustments of the reactance section l8and resistor 20 may be similar to those disclosed in the abovementionedapplication but for simplicity have been omitted from the presentdrawing.

The compensators l3 are energized in accordance with line-currents ofthe low-voltage circuit 2 by means of current transformers 22, and serveto introduce voltages in the secondary circuits of the potentialtransformers l2 proportional to the voltages consumed by the leakageimpedances of the power transformer 3, as explained in my c0- pendingapplication mentioned above.

The operation of the above described apparatus may best be understood byconsidering the circuit analytically. In the following, capital lettersare used to denote complex or vector quantities and lower case lettersare used as subscripts. The conjugate of any vector quantity is denotedby the corresponding capital letter surmounted by a circumflex accent.Scalar quantities are denoted by a capital letter surmounted by a bar.To simplify the equations, it is assumed that the ratio of eachstar-connected primary winding of the transformer 3 to the correspondingdelta-connected secondary winding is 1:1.

each phase of transformer 3, considered from delta side and assumed thesame for all phases.

ZS :secondary leakage impedance, or the part of Z caused by thetransformer secondary windings only, assumed the same for all phases.

Zx =the exciting impedance, or mutual impedance between primary andsecondary windings of each phase of transformer 3, assumed the same forall phases.

As the neutral point of the star-connected winding 4 is ungrounded, thehigh-voltage circuit l is three-phase three-wire, and the total powerflow therein may be measured as the sum of the conjugate products of thecurrents in any two phase conductors and the corresponding voltages ofthe two conductors with reference to the remaining conductor. Taking theb-phase conductor as reference, the total power flow is P whereNeglecting exciting current in the transformer 3, the primary voltagesare equal to the sum of the secondary voltages and the correspondingleakage impedance drops:

Eu '=Ea+[a' 'Z Eb"=Eb+Ib"Z (2) Ec"=Ec+Ic"Z Because of the star-deltavoltage relationship at the primary windings 4 of transformer 3 (seeFig. 2) the voltages Ea and E0 may be represented as Ea'=Ec"Eb"}' (3) E'=E E Substituting (2) in (3) The Equations (4) express the high-voltagequantities Ea and Ec' in terms of three voltages Ea, Eb and E0 of thelow-voltage circuit 2, and the three delta currents I a, I"b and I"ccirculating in the secondary windings 5. As the delta currents cannot beconveniently measured without special connections, it is preferable tosubstitute the secondary phase currents for the delta currents. Also, asthe circuit 2 is three-phase, three wire, one secondary current and onesecordary voltage may be eliminated from Equations (4:).

The relationship of currents at the junctions of the delta is Therelationship of voltages at the de1ta-connected windings 5 is, as shownvectorially in Fig. 2,

Eb=-Ea-'Ec (6) Substituting (5) and (6) in (4) and rearranging Equations('7) show that the phase-to-phase voltages of circuit i may be expressedas functions of two secondary phase-to-phase voltages and a secondaryphase current of circuit 2. However, as there is a circuit around thedelta which could carry a residual or zero-sequence current component,the polyphase quantities of circuit 2 can be completely expressed bythese variables only if the flow of zero-sequence current is prevented.It is therefore necessary to establish that no zero sequence currentcirculates in the delta for the above relationships to hold rigidly.

It will be noted that the terms IaZ and IBZ of Equations (7) above areeach derived from a plurality of terms of Equations (4) and appear assingle terms in (7) only because the same value of leakage impedance Zhas been assumed for all phases. As the terms IaZ and ICZ representcompensating voltages introduced by the compensators l3, it will beapparent that symmetrical leakage impedances Z of the power transformer3 are necessary for accurate compensation in accordance with theprinciple of the invention.

The voltages acting around the delta consist entirely of mutualimpedance drops derived from the primary phase currents, and theself-impedance drops of delta currents in the secondary leakageimpedances Z. The voltage equation the delta, accordingly, is

However as the high-voltage circuit I is assumed three-phase, threewire,

I'..'+Ib'+1c'=o (9) Substituting (9) in (8) and factoring I"+Ib"+Ic"=0(10) As the delta currents add to zero, there is no circulating currentin the delta which could disturb the relationships stated above. It willbe noted that Equation (8) holds only if the exciting impedance Zx issymmetrical in all phases and the secondary leakage impedance Z. issimilarly symmetrical. It may also be shown that symmetrical primaryleakage impedance of the transformer 3 is necessary to eliminate anyresidual component of the primary star voltages with reference to thejunction point of primary windings 4, in order to provide powermeasurements rigidly following Equation (1).

Fig. 3 shows a modified potential transformer arrangement which may besubstituted for the potential transformers ii of Fig. 1. In Fig. 3 thepotential transformers 25 are provided with two secondary windings" and21,0ne having twice the number of turns of the other. By properconnection of the windings 26 and 21, the two output potential circuitsmay be separately grounded, as may be desirable for energizingstar-connected measuring devices or for other reasons.

Fig. 4 shows an alternative construction of impedance drop compensatorwhich may be substituted for the compensators ii of Fig. 1. In

- the Fig. 4 construction, a parallel connection of the reactancesection 3| and the resistor 32 is employed, eliminating the necessityfor an auxiliary potential transformer, such as the transformer II ofFig. 1. l

I do not intend that the present invention shall be restricted to thespecific structural details, arrangement of parts or circuit connectionsherein set forth, as various modifications thereof may be eflectedwithout departing from the spirit and scope of my invention. I desire,therefore, that only such limitations shall be imposed as are indicatedin the appended claims.

I claim as my invention:

1. In an alternating-current system, apair of polyphase circuits,translating means including a closed circuit connected to all phases ofa first of said polyphase circuits' and having substantial- 1y uniformleakage impedance between all phases thereof, said closed circuit havingsubstantially uniform mutual impedance to all phases of the second ofsaid polyphase circuits, and means for deriving voltages of one of saidpolyphase circuits from the other thereof comprising phaseshifting meansfor correcting the shift of phase voltages in said translating means,and compensating means for correcting the leakage impedance voltage lossin said translating means.

' 2. In an alternating-current system, a pair of three-phase. circuits,translating meam including three-phase three-wire circuits,

a delta circuit connected to all phases of a first of said three-phasecircuits and having substantially uniform leakage impedance between allphases thereof, said delta circuit having substantially uniform mutualimpedance to all phases of the second of said three-phase circuits,andmeans for deriving phase voltages of one of said threephase circuitsfrom the other thereof comprising means for combining components ofdelta volt-- nected to said low-voltage circuits and star-con- I nectedwindings connected to said high-voltage circuit, said transformer meanshaving substantially uniform leakage impedance in said deltaconnectedwindings, substantially uniform leakage impedance in saidstar-connected'windings and substantially uniform exciting impedance inall phases, and means for deriving voltages of said high-voltage circuitfrom said low-voltage circuit comprising means for dividing two deltavoltages of said low-voltage circuit in equal components and for addingsaid components to undivided delta voltages in such manner as tosubstantially duplicate the phase voltages of said high-voltage circuitas to phase position, and compensating means for correcting the leakageimpedance voltage loss in said translating means.

4. In an alternating-current system, a pair of three-phase three-wirecircuits, transformer means having star-connected windings connected toone of said circuits and delta-connected windings connected to the otherof said circuits, said transformer means having constants such as tosubstantially exclude the circulation of zero sequence current in saiddelta-connected windings, and means for deriving voltages of one of saidthree-phase circuits from the other of said circuits includingcompensating impedances and means for energizing said compensatingimpedances in accordance with current quantities derived from the phasecurrents of said other of said circuits.

5. In an alternating-current system, a pair of transformer means havingstar-connected windings connected to one of said circuits anddelta-connected windings connected to the other of said circuits, saidtransformer means having constants such as to substantially exclude thecirculation of zero sequence current in said delta-connected windings,

EDWIN L. HARDER.

